Problem: Solve for $x$ : $x^2 - 7x + 6 = 0$
Explanation: The coefficient on the $x$ term is $-7$ and the constant term is $6$ , so we need to find two numbers that add up to $-7$ and multiply to $6$ The two numbers $-6$ and $-1$ satisfy both conditions: $ {-6} + {-1} = {-7} $ $ {-6} \times {-1} = {6} $ $(x {-6}) (x {-1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -6) (x -1) = 0$ $x - 6 = 0$ or $x - 1 = 0$ Thus, $x = 6$ and $x = 1$ are the solutions.